Question

An $\alpha$-particle and a proton are accelerated from rest by a potential difference of 100 V. After this, their de Broglie wavelengths are ${\lambda }_{\alpha }and{\lambda }_p$, respectively. The ratio ${\lambda }_p/{\lambda }_{\alpha },$ to the nearest integer, is ___

Answer 1

$\frac{1}{2}m{v}^2=qV$
$\frac{1}{2m}{p}^2=qV$
$p=\sqrt{2mqV}$
$\lambda =\frac{h}{p}$
$Ratioofwavelengths=\sqrt{8}=3$